Heritability Maximizing Dimensionality Reduction

The Model

• N individuals, indexed by i

• M variants, indexed by j

• K phenotypes, indexed by k

• h² = 0.5

• p_j ~ Uniform(0.05, 0.95)

• X_ij ~ Binomial(2, p)

• β_jk ~ Normal(0, h² / M)

• 𝓁_ik ~ X_ij · β_jk + Normal(0, √(1-h²))

• y_ik = f(𝓁_ik), where f is some non-linear function

Next Steps

• add noise to the images before training the model
• understand why the variance of trace-heritability after linear transformations is not zero; understand how this is related to variance explained between estimated and simulated latent phenotypes.
• scale up test setup (use more computers? speed up Balding-Nichols? ???)
• handle variants with non-zero LD
• handle samples with non-zero relatedness